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gold Here is an eTCL console program for spare parts in warranty period based on poisson distribution, lamda=1. Calculate spare parts in warranty period for 95% confidence level (eg. > 95%C). Calculations estimate spare parts or spare drives for a cloud backup system. This report references both the poisson and normal distributions, as implemented in TCL.
#pseudocode can be developed from rules of thumb.
#pseudocode: some problems can be solved by proportions (rule of three), to some order of magnitude
#pseudocode: enter quantity1, quantity2, quantity3 and expected output (quantity4) for testcases.
#pseudocode: enter time in years, number of remaining items
#pseudocode: output fraction of (remaining items) over (items at time zero)
#pseudocode: ouput remaining items as fraction or percent
#pseudocode: output fraction of (quantity4 ) over ( quantity1 at time zero)
#pseudocode: output fraction of (quantity2) * (quantity3 ) over (quantity1 at time zero)
#pseudocode: outputs should be in compatible units.
#pseudocode: rules of thumb can be 3 to 15 percent off, partly since g..in g..out.
#pseudocode: need test cases > small,medium, giant
#pseudocode: need testcases within range of expected operation.
#pseudocode: are there any cases too small or large to be solved?| table 1 | printed in | tcl wiki format |
|---|---|---|
| quantity | value | comment, if any |
| testcase number: | 1 | test of calculator lower limits |
| 400.0 : | MTBF mean time between failures in hours | warranty of parts, supplied with problem |
| 2.0 : | n quantity devices | warning!, testing lower_limit_N>10 |
| 0.003534: | lambda= failure rate per hour | supplied with problem |
| 1.4 : | expected failures on one part during warranty period | supplied with problem |
| 16.0 : | time interval days | warning!, testing lower_limit_days>90 |
| 1.645 : | 95%C percentile | ref. normal distribution |
| 0.04566 : | answers:MTBF in years | |
| 2190.0 : | AFR annualized failure rate percent/year | small lifetime gives many failures in year |
| 1.920 : | average failures from prorated AFR over time interval | |
| 4 : | home brew solution spares from poisson, 95%C percentile | supplied with problem |
| 4.199 : | required spares from normal distribution over time interval | round up to 5 |
| 4 or 5 : | 95%C spares from both poisson and normal d. | seem reasonably close |
| 4 ot 5 > 1.4 : | 95%C spares > expected5 failures in 16 day interval | 95%c spares about 3*failures |
| textbook table solution gives 4 spares | warranty=400 hours | 1.4 failures in 400 hours | 0.003534 f/hr | 16 days interval | MTTF=283 hours |
|---|---|---|---|---|---|
| from real_life problem | poi. & nor. distributions from CRC rubber & textbook tables | ||||
| probability of X row >>> | p(0) | p(1) | p(2) | p(3) | p(4) |
| textbook poisson cdf,L=1 | .3679 | .7358 | .9197 | .9810 | .9963 |
| textbook poisson pdf,L=1 | .3679 | .3679 | .1839 | .0613 | .0153 |
| textbook normal cdf,S=1 | .5000 | .8413 | .9773 | .9987 | 1.0 |
| textbook normal pdf,S=1 | .3989 | .2420 | .0540 | .0044 | .0001 |
| solution of 4 spares > 95% | 4 spares col. ^^^^ | ||||
| % difference in cum. curves | 14.3% | 6.2% | 1.8% | 0.37% |
# pretty print from autoindent and ased editor
# written on Windows XP on eTCL
# working under TCL version 8.6.2 and_or eTCL 1.0.1
# gold on TCL WIKI, 5nov2014
# Console program for spare parts in warranty period
# based on poisson distribution, lamda=1
# calculate spare parts for 95% confidence level (eg. > 95%C).
package require Tk
namespace path {::tcl::mathop ::tcl::mathfunc}
console show
proc poissionx {warranty_hours failure_rate_hours percentile} {
set parts_prob 0
set percentile_factor [* $percentile 1.E-2 ]
foreach item { 1 2 3 4 5 6 7 8 9 10 } {
set exponent [* $warranty_hours $failure_rate_hours -1. ]
set parts_prob [+ $parts_prob [exp $exponent ] ]
puts "spares $item prob. $parts_prob /n
product warranty_hours $warranty_hours /n
failure_rate_per_hours $failure_rate_hours MTTF=1/L=283 hours /n
average failures across warranty period is 400/283 or 1.4 /n
simple replacement would rounded 1.4 or 2 spares at approx. 50%C /n
additional spares needed for 95%C "
if { $parts_prob > $percentile_factor } { return $item } }
return 0 }
puts " poission spare parts from home_brew [ poissionx 400. 0.003534 95 ] "
puts " 4 spares are required for above 95 percent confidence level "
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